Cardiac cell modelling: Observations from the heart of the cardiac physiome project

Fink, Martin; Niederer, Steven A.; Cherry, Elizabeth M.; Fenton, Flavio H.; Koivumäki, Jussi T.; Seemann, Gunnar; Thul, Ruediger; Zhang, Henggui; Sachse, Frank B.; Beard, Dan; Crampin, Edmund J.; Smith, Nicolas P.

doi:10.1016/j.pbiomolbio.2010.03.002

Cited by 146 publications

(137 citation statements)

References 220 publications

(206 reference statements)

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“…In this paper, we will use the bifurcation analysis similar to [12][13][14] to study the system introduced in [1]. We want to highlight that we can use our approach to investigate also more complex models, see for instance [15][16][17]. The numerical effort will be higher but we can use this basic principle for further studies.…”

Section: Introductionmentioning

confidence: 99%

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Bifurcation Analysis of a Certain Hodgkin-Huxley Model Depending on Multiple Bifurcation Parameters

Erhardt

2018

Mathematics

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Abstract:In this paper, we study the dynamics of a certain Hodgkin-Huxley model describing the action potential (AP) of a cardiac muscle cell for a better understanding of the occurrence of a special type of cardiac arrhythmia, the so-called early afterdepolarisations (EADs). EADs are pathological voltage oscillations during the repolarisation or plateau phase of cardiac APs. They are considered as potential precursors to cardiac arrhythmia and are often associated with deficiencies in potassium currents or enhancements in the calcium or sodium currents, e.g., induced by ion channel diseases, drugs or stress. Our study is focused on the enhancement in the calcium current to identify regions, where EADs related to enhanced calcium current appear. To this aim, we study the dynamics of the model using bifurcation theory and numerical bifurcation analysis. Furthermore, we investigate the interaction of the potassium and calcium current. It turns out that a suitable increasing of the potassium current adjusted the EADs related to an enhanced calcium current. Thus, one can use our result to balance the EADs in the sense that an enhancement in the potassium currents may compensate the effect of enhanced calcium currents.

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Section: Introductionmentioning

confidence: 99%

“…Furthermore, we want to refer to the review article on cardiac cell modelling [16], where the authors give a nice overview on existing cardiac cell models, as well as to the review article on cardiac tissue modelling [15].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of a Certain Hodgkin-Huxley Model Depending on Multiple Bifurcation Parameters

Erhardt

2018

Mathematics

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“…The impact of cardiac electrophysiology simulations across an expanded range of applications has seen an increase in model complexity through increasing numbers of equations to describe cellular and sub-cellular functions [8], regionspecific parameter sets for cell models [9,10] and high-resolution meshes to capture anatomical detail [11]. Distinct from the development of new models is the corresponding development of simulation codes that solve numerically the equations of a given model.…”

Section: Introductionmentioning

confidence: 99%

Verification of cardiac tissue electrophysiology simulators using an N -version benchmark

Niederer

Kerfoot

Benson

et al. 2011

Phil. Trans. R. Soc. A.

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One contribution of 11 to a Theme Issue 'Towards the virtual physiological human: mathematical and computational case studies'. Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.

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“…The non-linear reaction term I ion and the ODE system for the gating variables w and the ionic concentrations c are given by the ionic membrane model; see e.g. [16,56] for recent reviews. Here we will consider the Luo−Rudy I (LR1) membrane model [21].…”

Section: Continuous Modelmentioning

confidence: 99%

A comparison of coupled and uncoupled solvers for the cardiac Bidomain model

2013

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Abstract. The aim of this work is to compare a new uncoupled solver for the cardiac Bidomain model with a usual coupled solver. The Bidomain model describes the bioelectric activity of the cardiac tissue and consists of a system of a non-linear parabolic reaction-diffusion partial differential equation (PDE) and an elliptic linear PDE. This system models at macroscopic level the evolution of the transmembrane and extracellular electric potentials of the anisotropic cardiac tissue. The evolution equation is coupled through the non-linear reaction term with a stiff system of ordinary differential equations (ODEs), the so-called membrane model, describing the ionic currents through the cellular membrane. A novel uncoupled solver for the Bidomain system is here introduced, based on solving twice the parabolic PDE and once the elliptic PDE at each time step, and it is compared with a usual coupled solver. Three-dimensional numerical tests have been performed in order to show that the proposed uncoupled method has the same accuracy of the coupled strategy. Parallel numerical tests on structured meshes have also shown that the uncoupled technique is as scalable as the coupled one. Moreover, the conjugate gradient method preconditioned by Multilevel Hybrid Schwarz preconditioners converges faster for the linear systems deriving from the uncoupled method than from the coupled one. Finally, in all parallel numerical tests considered, the uncoupled technique proposed is always about two or three times faster than the coupled approach.Mathematics Subject Classification. 65N55, 65M55, 65F10, 92C30.

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Cardiac cell modelling: Observations from the heart of the cardiac physiome project

Cited by 146 publications

References 220 publications

Bifurcation Analysis of a Certain Hodgkin-Huxley Model Depending on Multiple Bifurcation Parameters

Bifurcation Analysis of a Certain Hodgkin-Huxley Model Depending on Multiple Bifurcation Parameters

Verification of cardiac tissue electrophysiology simulators using an N -version benchmark

A comparison of coupled and uncoupled solvers for the cardiac Bidomain model

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